Question: Solve for $x$ : $6x^2 - 18x - 60 = 0$
Solution: Dividing both sides by $6$ gives: $ x^2 {-3}x {-10} = 0 $ The coefficient on the $x$ term is $-3$ and the constant term is $-10$ , so we need to find two numbers that add up to $-3$ and multiply to $-10$ The two numbers $-5$ and $2$ satisfy both conditions: $ {-5} + {2} = {-3} $ $ {-5} \times {2} = {-10} $ $(x {-5}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x + 2) = 0$ $x - 5 = 0$ or $x + 2 = 0$ Thus, $x = 5$ and $x = -2$ are the solutions.